Total Variation Approximation of Random Orthogonal Matrices by Gaussian Matrices

  • Kathryn StewartEmail author


The topic of this paper is the asymptotic distribution of the entries of random orthogonal matrices distributed according to Haar measure. We examine the total variation distance between the joint distribution of the entries of \(W_n\), the \(p_n \times q_n\) upper-left block of a Haar-distributed matrix, and that of \(p_nq_n\) independent standard Gaussian random variables and show that the total variation distance converges to zero when \(p_nq_n = o(n)\).


Random orthogonal matrix Central limit theorem Wishart matrices Moments 

Mathematics Subject Classification (2010)

60F05 60C05 



The results of this paper are part of a Ph.D. thesis written under the direction of Elizabeth Meckes; the author very much thanks her for many helpful conversations.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA

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